{
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "# Jump with Chebyshev Nodes"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 1,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "import numpy as np\n",
        "import numpy.linalg as la\n",
        "import matplotlib.pyplot as pt\n",
        "import scipy.special as sps"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 2,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f74680949b0>]"
            ]
          },
          "execution_count": 2,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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c4VBVF860LMneJKdU1d4kpwLPDCjbCUz0za8B7gd+Bjg3yZPAq4CTk9xXVe+aaX2Tk5MH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\nahgOkqSG4SBJavw//v2ak46okqQAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f746812e438>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "n = 50\n",
        "\n",
        "k = np.arange(1, n+1, dtype=np.float64)\n",
        "\n",
        "cheb_nodes = np.cos((2*k-1)/(2*n)*np.pi)\n",
        "pt.plot(cheb_nodes, 0*cheb_nodes, \"o\")"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Build the Vandermonde matrix for orthogonal polynomials with Chebyshev nodes:"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 3,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "13.082290511123743"
            ]
          },
          "execution_count": 3,
          "metadata": {},
          "output_type": "execute_result"
        }
      ],
      "source": [
        "V = np.array([\n",
        "    sps.eval_legendre(i, cheb_nodes)\n",
        "    for i in range(n)\n",
        "]).T\n",
        "\n",
        "la.cond(V)"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {},
      "source": [
        "Notice the condition number of the Vandermonde matrix! How does that compare to our prior ones?"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 4,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "def f(x):\n",
        "    return (x>=0).astype(np.float64)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 5,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "coeffs = la.solve(V, f(cheb_nodes))"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 6,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "x = np.linspace(-1, 1, 1000)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 7,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": [
        "interpolant = 0\n",
        "for i in range(n):\n",
        "    interpolant += coeffs[i]*sps.eval_legendre(i, x)"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": 8,
      "metadata": {
        "collapsed": false
      },
      "outputs": [
        {
          "data": {
            "text/plain": [
              "[<matplotlib.lines.Line2D at 0x7f746812e080>]"
            ]
          },
          "execution_count": 8,
          "metadata": {},
          "output_type": "execute_result"
        },
        {
          "data": {
            "image/png": 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HFckLVQdJIclFm0A3YEnc8lJCYIg3DphmZt8DioBTc3BckbxQEJBCkosgkGy+isQJgM4H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\n",
            "text/plain": [
              "<matplotlib.figure.Figure at 0x7f746812e0b8>"
            ]
          },
          "metadata": {},
          "output_type": "display_data"
        }
      ],
      "source": [
        "pt.plot(x, interpolant)\n",
        "pt.plot(x, f(x), \"--\", color=\"gray\")"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "collapsed": false
      },
      "outputs": [],
      "source": []
    }
  ],
  "metadata": {
    "kernelspec": {
      "display_name": "Python 3",
      "language": "python",
      "name": "python3"
    },
    "language_info": {
      "codemirror_mode": {
        "name": "ipython",
        "version": 3
      },
      "file_extension": ".py",
      "mimetype": "text/x-python",
      "name": "python",
      "nbconvert_exporter": "python",
      "pygments_lexer": "ipython3",
      "version": "3.5.1+"
    }
  },
  "nbformat": 4,
  "nbformat_minor": 0
}